Existence theorems for the one-dimensional singular p-Laplacian equation with a nonlinear boundary condition

Authors:
Haishen Lü;Donal O'Regan;Ravi P. Agarwal
Affiliations:
Department of Applied Mathematics, Hohai University, Nanjing 210098, China;Department of Mathematics, National University of Ireland, Galway, Ireland;Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

In this paper, general existence theorems are presented for the singular equation -(ϕp(y'))' = q(t)f(t, y), 0 t y(0) = 0, Ψ(y(1)) + y'(1) = 0. Throughout, our nonlinearity is allowed to change sign. The singularity may occur at y = 0, t =0 and t = 1. In addition, Ψ may be nonlinear.